Finite Group Databasebeta

← C2×#10593328 #11858259

Subgroups — C2×#10593328 #11858259

Order 1152.

874 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#157C211yesmaximal, characteristic
2C2×#63818C212yesmaximal
3#10593328C218yesmaximal, direct product factor
4C2×#63732C214yesmaximal, complemented
5C23×#157C412yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C4×#157C411yescharacteristic
8C2×C4×#157C414yes—
9C2×C4×#157C411yescharacteristic
10C2×C4×#157C2212yes—
11C2×C4×#157C2214yes—
12C2×C3×#208—22no—
13C2×#3712—22no—
14#63818—24no—
15#63818C2218yes—
16C2×#3710C2214yes—
17#63732C22116yescomplemented
18C2×D3×M16—62no—
19C23×C3⋊D3C2×C411yescharacteristic
20C22×#157—28no—
21C22×#157C2×C412yes—
22C22×#157C2×C418yes—
23C22×#157C2×C412yes—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3Q811yescharacteristic
26C2×C4×C3⋊D3C2×C412yes—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3D412yes—
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3Q811yescharacteristic
31C2×C4×C3⋊D3Q812yes—
32C2×C4×C3⋊D3C2311yescharacteristic
33C2×C4×C3⋊D3C2312yes—
34C4×#157C2×C414yes—
35C4×#157C2×C414yes—
36C4×#157C2×C414yes—
37C4×#157C2314yes—
38C3×#208—28no—
39C2×C3×C3⋊C8—24no—
40#3712—28no—
41#3710—24no—
42#3710C2318yes—
43C2×#423—91nomaximal, Sylow
44C22×C4×D3—62no—
45C2×C3×M16—62no—
46C2×#208—22no—
47D3×M16—68no—
48D3×M16—68no—
49C2×ΓL(1,𝔽25)—64no—
50C2×D3×C8—64no—
51C23×C32C4⋊C411yescharacteristic
52C22×C3⋊D3—24no—
53C22×C3⋊D3C4⋊C411yescharacteristic
54C22×C3⋊D3C4⋊C412yes—
55C22×C3⋊D3C22×C412yes—
56C22×C3⋊D3C22×C411yescharacteristic
57C2×#157—24no—
58C2×#157—216no—
59C2×#157M1618yescomplemented
60C2×#157C22×C414yes—
61C2×#157C22×C414yes—
62C2×C32×C4C4⋊C412yes—
63C2×C32×C4C4⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×D412yes—
66C2×C3⋊Dic3C4⋊C412yes—
67C2×C3⋊Dic3C4⋊C411yescharacteristic
68C2×C3⋊Dic3C2×Q812yes—
69C2×C3⋊Dic3C2×Q811yescharacteristic
70C4×C3⋊D3C4⋊C412yes—
71C4×C3⋊D3C4⋊C412yes—
72C4×C3⋊D3C4⋊C412yes—
73C4×C3⋊D3C22×C411yescharacteristic
74C4×C3⋊D3C22×C412yes—
75C4×C3⋊D3C2×D411yescharacteristic
76C4×C3⋊D3C2×D412yes—
77C4×C3⋊D3C2×Q812yes—
78C4×C3⋊D3C2×Q811yescharacteristic
79C4×C3⋊D3C2411yescharacteristic
80C3×C3⋊C8—28no—
81C22×M16—92no—
82C22×C42—91no—
83#423—98no—
84C2×C4⋊C8—94no—
85C23×D3—62no—
86C22×C3×C4—22no—
87C22×Dic3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—64no—
91C2×C4×D3—64no—
92C2×C4×D3—62no—
93C2×C4×D3—64no—
94C2×C4×D3—64no—
95C2×C4×D3—62no—
96C3×M16—68no—
97C2×C3×C8—64no—
98#208—28no—
99C2×C3⋊C8—24no—
100ΓL(1,𝔽25)—616no—
101D3×C8—68no—
102D3×C8—68no—
103C22×C32—22no—
104C22×C32C2×C4⋊C412yes—
105C22×C32C2×C4⋊C411yescharacteristic
106C2×C3⋊D3—22no—
107C2×C3⋊D3—24no—
108C2×C3⋊D3—24no—
109C2×C3⋊D3C2×C4⋊C412yes—
110C2×C3⋊D3C2×C4⋊C411yescharacteristic
111C2×C3⋊D3C2×M1614yes—
112C2×C3⋊D3C23×C411yescharacteristic
113#157—24no—
114#157C2×M1618yescomplemented
115C32×C4C2×C4⋊C411yescharacteristic
116C32×C4C2×C4⋊C412yes—
117C32×C4C22×D411yescharacteristic
118C3⋊Dic3C2×C4⋊C411yescharacteristic
119C3⋊Dic3C2×C4⋊C412yes—
120C3⋊Dic3C22×Q811yescharacteristic
121C23×C4—91no—
122C23×C4—92no—
123C2×M16—62no—
124C2×M16—98no—
125C2×M16—182no—
126C2×M16—184no—
127C22×C8—94no—
128C2×C42—91no—
129C2×C42—94no—
130C2×C42—91no—
131C2×C42—92no—
132C2×C42—94no—
133C4⋊C8—916no—
134C23×C3—22no—
135C22×D3—62no—
136C22×D3—64no—
137C22×D3—62no—
138C22×D3—64no—
139C22×D3—128no—
140C2×C3×C4—24no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—24no—
144C2×Dic3—62no—
145C2×Dic3—64no—
146C2×Dic3—62no—
147C2×Dic3—64no—
148C4×D3—64no—
149C4×D3—64no—
150C4×D3—64no—
151C4×D3—62no—
152C4×D3—64no—
153C4×D3—62no—
154C4×D3—64no—
155C4×D3—62no—
156C4×D3—64no—
157C4×D3—62no—
158C3×C8—68no—
159C3⋊C8—28no—
160C2×C32—22no—
161C2×C32#42312yescomplemented
162C2×C32C22×C4⋊C411yescharacteristic
163C3⋊D3—22no—
164C3⋊D3#42312yescomplemented
165C3⋊D3C22×M1612yes—
166C24—91no—
167C22×C4—92no—
168C22×C4—91no—
169C22×C4—92no—
170C22×C4—92no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—92no—
175C22×C4—92no—
176C22×C4—91no—
177C22×C4—98no—
178C22×C4—92no—
179C22×C4—188no—
180C22×C4GO+(4,𝔽2)11yescharacteristic
181M16—68no—
182M16—188no—
183C2×C8—64no—
184C2×C8—98no—
185C2×C8—184no—
186C42—94no—
187C42—94no—
188C42—94no—
189C42—94no—
190C22×C3—22no—
191C22×C3—24no—
192C22×C3—44no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—68no—
196C2×D3—64no—
197C2×D3—128no—
198C2×D3—128no—
199C2×D3—124no—
200C3×C4—22no—
201C3×C4—24no—
202C3×C4—22no—
203Dic3—62no—
204Dic3—64no—
205Dic3—62no—
206C32C2×#42311yescharacteristic, complemented, Sylow
207C23—91no—
208C23—92no—
209C23—92no—
210C23—91no—
211C23—184no—
212C23#377311yescharacteristic
213C2×C4—94no—
214C2×C4—98no—
215C2×C4—92no—
216C2×C4—92no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—92no—
227C2×C4—91no—
228C2×C4—92no—
229C2×C4—94no—
230C2×C4—1816no—
231C2×C4—184no—
232C2×C4#377311yescharacteristic
233C2×C4#377312yes—
234C2×C4C2×GO+(4,𝔽2)12yes—
235C2×C4C2×GO+(4,𝔽2)11yescharacteristic
236C8—68no—
237C2×C3—24no—
238C2×C3—22no—
239C2×C3—44no—
240D3—64no—
241D3—64no—
242D3—124no—
243C22—22no—
244C22—94no—
245C22—91no—
246C22—91no—
247C22—92no—
248C22—184no—
249C22—184no—
250C22—182no—
251C22C2×#377312yes—
252C22C2×#377311yescharacteristic
253C4—98no—
254C4—91no—
255C4—91no—
256C4—92no—
257C4—184no—
258C4C2×#377312yes—
259C4C2×#377311yescharacteristic
260C4C22×GO+(4,𝔽2)11yescharacteristic
261C3—22no—
262C2—22no—
263C2—92no—
264C2—92no—
265C2—182no—
266C2#1059332812yesdirect product factor
267C2C22×#377311yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#423
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #10593328C2direct (N × H)
4. C2×#63732C2semidirect
17. #63732C22semidirect
59. C2×#157M16semidirect
114. #157C2×M16semidirect
161. C2×C32#423semidirect
164. C3⋊D3#423semidirect
206. C32C2×#423semidirect
266. C2#10593328direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4×#1572
C2×#638182
#105933282
C2×#637322
C2×#4239